Prime minister Fukuda resigns after one year in the job. He takes his new cabinet with him, only weeks after a cabinet reshuffle. It's not surprising that something would happen fairly soon; the job was looking increasingly hopeless, with support rate in the 20's, conflict between the LDP and its coalition partner New Komeito and waning support from within his own party. The real question, I think, is why now and not in December, and why he resigned, not called an election.
As prime minister he really has two options if the situation is untenable. He can resign or he can call a general election. They are solutions to very different problems and which he'd do depends on what he perceives to be the main problem. If the problem is external - an unworkable parliamentary situation for instance, low support numbers or flagging support from coalition partners - then the right response is to call a general election and take the case to the voters. If the problem is internal, such as lack of support from within his own party or intra-party conflicts that hamstrings the cabinet, then he can resign and let the party select a leader that can resolve those internal issues.
There is also a psychological aspect: if you call an election and lose it, you're perceived as a fighter, someone who went down swinging. If you quit, then, well, you're just a quitter. A common sentiment yesterday was disappointment that he would give up and no go on until the bitter end. Fukuda probably had some fairly strong reasons to choose to resign in other words, and I think that the main reason is Aso Taro.
Aso has run for the prime minister post in the LDP twice, first two years ago when Abe won, then last year hen Fukuda was elected prime minister. In both cases it seemed he was overreaching - overestimating his own popularity and dismissing his opponents. Aso is the choice of the right wing of the party and has been grooming himself for the prime minister post for years. He is prone to inflammatory and careless statements, which doesn't bode well for a prime ministership (though it does make for entertaining political blogging). In the year since his last defeat he's been taking constant potshots at Fukuda and his cabinet, frequently harming the LDP along the way. Last month Fukuda reshuffled his cabinet and appointed Aso secretary general of the LDP. This was probably intended as a quid pro quo: Aso stops fighting the Fukuda cabinet and starts working with the team; in exchange he gets a prestigious position from which he'll be well set to launch his own campaign when Fukuda leaves.
That did not work as intended. Aso has just used the secretary general post as a convenient perch from which to launch ever more public challenges to Fukuda, including setting public support numbers for when Fukuda should give up. If you get the impression of a selfish brat used to always get his own way, then you're picking up the same vibes I do.
I vaguely suspect that Aso's scenario for the fall went something like this: Fukuda soldiers on with the fall legislative session, gives up and calls an election (the election needs to be called no later than next year in any case). The LDP gets trampled - possibly even losing the government to a DPJ-led coalition - and Fukuda dutifully falls on his sword. Aso becomes the new prime minister candidate for the LDP and reassembles the pieces while he waits a few months to a year until the DPJ implodes in internal conflict. He then leads the now purged and resurgent hawkish LDP into a new era of political dominance with himself as its saviour and undisputed lifetime leader. I'm pretty sure square-jawed bronze statues and "Dear Leader" homilies figure somewhere in there as well.
Instead, what Fukuda has done is to say "Blow this, I'm too old and too weary to deal with this anymore. You'll find me at the golf course, I'm the guy in the loud pants and happy, contented smile. Here, Aso, this unholy mess is all yours to fix." Aso is now looking to be the guy who will lead the LDP into the coming election, and unless he can pull some mighty big rabbits out of a very small hat he is looking at presiding over a historical defeat. If LDP loses badly and DPJ is able to form a stable government he'll be looking forward to an even shorter stint in the driver's seat than either of his rivals, and be remembered only as the guy who cost LDP the reins of power.
Now, he is quite popular (he polls even with "none of the above", which is good in Japanese politics), he'll have a substantial popularity boost as the new guy on top so it is quite feasible he'll be able to avert disaster and limit the election loss. But seems now that if he wants to be the saviour of the LDP and not just another caretaker he will have to pull off a real miracle to do it.
Edit: Tobias Harris of Observing Japan makes a similar point, and believes Aso is poised for failure and LDP in dire straits. Jun Okumura of Globaltalk 21 sees it a little differently; with DPJ leader Ozawa Ichiro's lousy popularity numbers he predicts Aso will muddle through more or less by default. We'll see.